Application of numerical inverse Laplace transform algorithms in fractional calculus
Application of numerical inverse Laplace transform algorithms in fractional calculus
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DOI：
10.1016/j.jfranklin.2010.11.009
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发表时间：
2011-03
期刊：
影响因子：
--
通讯作者：
H. Sheng;Yan Li;Y. Chen
中科院分区：
文献类型：
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作者：
H. Sheng;Yan Li;Y. Chen
拉普拉斯变换技术被认为是求解整数阶微分方程组的一种有效方法。但对于非整数阶的微分方程组，拉普拉斯变换技术只对相对简单的方程有效，这是因为拉普拉斯变换的逆运算比较困难。为了找到一种简单的方法来数值求解复杂的分数阶微分方程组，我们研究了数值拉普拉斯逆变换算法在分数阶微积分中应用的有效性。利用分数阶方程的拉普拉斯变换对三种数值拉普拉斯逆变换算法INVLAP、GAVSTEH和NILT进行了测试。通过与数值拉普拉斯逆变换算法结果的比较，验证了分数阶常微分方程组数值拉普拉斯逆变换算法的有效性和可靠性。
Laplace transform technique has been considered as an efficient way in solving differential equations with integer-order. But for differential equations with non-integer order, the Laplace transform technique works effectively only for relatively simple equations, because of the difficulties of calculating inversion of Laplace transforms. Motivated by finding an easy way to numerically solve the complicated fractional-order differential equations, we investigate the validity of applying numerical inverse Laplace transform algorithms in fractional calculus. Three numerical inverse Laplace transform algorithms, named Invlap, Gavsteh and NILT, were tested using Laplace transforms of fractional-order equations. Based on the comparison between analytical results and numerical inverse Laplace transform algorithm results, the effectiveness and reliability of numerical inverse Laplace transform algorithms for fractional-order differential equations was confirmed.